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Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblem 47
Chapter 1, Problem 47

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
cot πœ‹/12

Verified step by step guidance
1
Recognize that the problem asks for \( \cot \frac{\pi}{12} \), which is the cotangent of \( \frac{\pi}{12} \) radians. Cotangent is the reciprocal of tangent, so \( \cot x = \frac{1}{\tan x} \).
Convert the angle \( \frac{\pi}{12} \) radians to degrees if needed for your calculator. Since \( \pi \) radians equals 180 degrees, \( \frac{\pi}{12} = \frac{180}{12} = 15^\circ \).
Use the calculator to find \( \tan 15^\circ \). Make sure your calculator is set to degree mode if you use degrees, or radian mode if you input the angle in radians.
Calculate the cotangent by taking the reciprocal of the tangent value: \( \cot \frac{\pi}{12} = \frac{1}{\tan \frac{\pi}{12}} \).
Round the result to four decimal places as requested.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding the Cotangent Function

Cotangent is a trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle, or equivalently, cot(ΞΈ) = 1/tan(ΞΈ). It is the reciprocal of the tangent function and is used to find angles or side ratios in trigonometry.
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Introduction to Cotangent Graph

Radian Measure and Angle Conversion

Angles in trigonometry can be measured in degrees or radians. The given angle Ο€/12 is in radians, where Ο€ radians equal 180 degrees. Understanding how to interpret and convert radians is essential for evaluating trigonometric functions accurately.
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Converting between Degrees & Radians

Using a Calculator for Trigonometric Values

Calculators can compute trigonometric functions directly in radians or degrees. To find cot(Ο€/12), one typically calculates tan(Ο€/12) first and then takes its reciprocal. Ensuring the calculator is set to the correct mode (radians) is crucial for accurate results.
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How to Use a Calculator for Trig Functions
Related Practice
Textbook Question

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-5πœ‹/4

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Textbook Question

In Exercises 44–48, find the reference angle for each angle.

- 11πœ‹/3

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Textbook Question

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-7πœ‹/4

1
views
Textbook Question

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-5πœ‹/6

1
views
Textbook Question

In Exercises 44–48, find the reference angle for each angle.

-410Β°

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Textbook Question

In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

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